Addition to Lemma 81. In [1], § 4, there is a variant of the matrix formula (64) for the simple continued fraction of a real number. Given integers a0, a1, . . . with ai > 0 for i ≥ 1 and writing, for n ≥ 0, as usual, pn/qn = [a0, a1, . . . , an], one checks, by induction on n, the two formulae ( 1 a0 0 1 )( 1 0 a1 1 ) · · · ( 1 an 0 1 ) = ( pn−1 pn qn−1 qn ) if n is even ( 1 a0 0 1 )( 1 0 a1 1...

Through a case study of Ghana’s TradeNet, a business-to-government (B2G) Electronic Data Interchange (EDI) implemented to automate and integrate customs clearance, this article investigates ‘irrationalities’ of IT-enabled change in the context of a developing country bureaucracy. Our data revealed that despite TradeNet’s potential for full automation and integration, bureaucrats sometimes prefe...

Recent writers have invoked the idea that epistemic rationality gives us options in an attempt to show that we can exercise direct doxastic control without irrationality. Speci cally, they suggest that when the evidence for p is su cient but not conclusive, it would be rational either to believe p or to be agnostic on p, and they hold that we can in these cases e ectively decide to form either ...

It remains unclear if patients with different types of common mental disorders, such as adjustment, anxiety and depressive disorders, have the same irrational ideas. The aim of this prospective cohort study (n = 190) is to investigate differences in level and type of irrational beliefs among these groups and to examine whether a change in irrational beliefs is related to symptom recovery. Irrat...

1. Introduction. The irrationality of values of the zeta-function ζ(s) at odd integers s ≥ 3 is one of the most attractive problems in number theory. Inspite of a deceptive simplicity and more than two-hundred-year history of the problem, all done in this direction can easily be counted. It was only 1978, when Apéry [A] obtained the irrationality of ζ(3) by a presentation of " nice " rational a...

Perception is often categorical: the perceptual system selects one interpretation of a stimulus even when evidence in favor of other interpretations is appreciable. Such categorization is potentially in conflict with normative decision theory, which mandates that the utility of various courses of action should depend on the probabilities of all possible states of the world, not just that of the...

This paper explores the question of whether an agent can freely and willfully act against her all-things-considered best judgment. I construct the case of an agent acting against the demands of impartial morality that give her decisive reason to act, without compromising her full agential power and strong will. I call this her demonstration of free irrationality and distinguish it from the acco...

In a recent paper a new direct proof for the irrationality of Euler's number e = ∞ k=0 1 k! and on the same lines a simple criterion for some fast converging series representing irrational numbers was given. In the present paper, we give some generalizations of our previous results. 1 Irrationality criterion Our considerations in [3] lead us to the following criterion for irrationality, where x...